# Referee Response: Log Patents Definition Audit

## Definition
- `log_patents` = **ln(patents)**
- patent_total: mean=16406, median=392, min=1, max=439175
- log_patents: mean=6.393, SD=2.674

## Within-Country Variation
- Within-country SD of Z_1: **0.2699**

## Economic Interpretation of Z_1 Coefficient (-6.91)

| Scenario | ΔZ_1 | Δlog(patents) | % Δ patents |
|---|---|---|---|
| 1 within-SD | 0.2699 | -1.865 | -84.5% |
| 20-year aging | 0.27 | -1.866 | -84.5% |

The coefficient of -6.91 is NOT "9.4 log-points" for any plausible demographic shift. A 1 within-SD increase in Z_1 (0.270) implies a 85% change in patent counts. Over a 20-year aging window (ΔZ_1 ≈ 0.27), the implied change is -84.5%.

*Note: The referee may have multiplied the coefficient by a 1-unit change in Z_1, which is ~4× the within-country SD and outside observed variation.*
